Hi there I'm having a bit of a conceptual difficulty regarding the equations for inelastic collisions. Suppose a body of mass M1, moving at initial velocity V1, collides and sticks to another body, mass M2, moving at some other initial velocity V2. They then move together with a final velocity of V3. Now I understand that in this situation, kinetic energy is not conserved, though momentum (of the two-particle system) is. I also know that the "missing" kinetic energy must have gone into the production of sound waves, or thermal energy, changes of potential energy (if the bodies deform?) etc. If only because this is what I am taught. If we suppose that V3 is the only unknown in the above problem, then I can quite easily calculate the magnitude of V3 from the other data (suppose that the collision is linear, to simplify things). Then it is also easy to calculate the final kinetic energy of the two-body system. I've done these problems countless times so no difficulty in the calculatiions. But what I can't understand: how is it that these simple conservation-of-linear-momentum equations "know" that kinetic energy is not conserved? Surely there would be a hypothetical magnitude for V3 such that kinetic energy would (hypothetically) be conserved -- how do these equations correctly produce a a V3 such that kinetic energy is NOT conserved? In fact, working symbolically with the conservation of momentum equations, I can sort of see why the system's kinetic energy would be decreased, in such a collision. Still, conceptually, I am not happy about how this all gets built into these equations. Thanks in advance!